# Similarity of Structure (was Memory Merging Possible for Close Duplicates)

From: Lee Corbin (lcorbin@rawbw.com)
Date: Mon Mar 17 2008 - 17:45:37 MDT

Mike Dougherty wrote

> Your definition of similar is not sufficient for me to make sense of
> your bit string analogy. I "get" that there might be some reference
> to TM or Life Board in there, but I'd have to guess too much.

Let's see. I wrote

> What determines how close a duplicate is to the original?
[An excellent question, by the way.]
> Whether the TE uses teleportation or computronium uploads,
> the principle measure of identity is ... what exactly?

It is similarity of structure, ultimately. Of course, we have various
measures of that (but we also have various yard-sticks that differ
one from the other a little, and even meter-sticks, but we firmly
believe in the utility of the 'length' concept, despite the dance of
atoms going on in physical objects).

Suppose that by some *obvious* [1] isomorphism, today Lee is
one bit string

11011011001110010110111111001010110100000011...
and tomorrow I am
11011011001110010110011111001010110100000010...

where two 0's happen to be changed to 1's. By all measures
of similarity, those two strings are still very similar. (It would be
easy to mention some particular measures used by mathematicians,
but the ones I'm completely familiar with without having to go look
them up aren't very applicable here.)

I don't think that I *defined* exactly what "similar" means, (which is
usually a good idea not to try), but okay, so we know from countless
examples in daily life when two things are similar, or are comparatively
similar relative to some other comparison. The idea is for this very
commonplace notion to be supplemented by various "measures"
quite in analogy to how our ancestors' notions of hot and cold were
eventually supplemented by the development of the concept of
temperature and various apparati (which google seems to think ok
for the plural form), such as thermometers. To be sure, this did not
exactly correspond with our ancestors' intuitions in all cases (for
example when they found water to feel very warm after they'd been
out in the cold a long time).

Sorry if the preceding paragraph just belabors the obvious.

Anyway, so information theorists looked for simpler structures in which
*similarity* might be easier to quantify. Thus they came up with the
measures I alluded to. Now I can sort of imagine this being extended
to more complex structures. Suppose we wanted to know as well as
we could how similar two electrical resistors were. Assuming the
easiest case first, let's say that they weigh the same and have no gross
obvious differences, even to the point where the investigators suspect
that they may be almost *exactly* identical.

The next paragraph will show that I'm *not* a materials scientist! :-)

They may be able to strip off micrometer thick cylindrical sections
and directly compare them to the "same" sections of the other. Let's
say that the first section of each was really a coat of paint. Now we
have (in principle, here, far from practice I think) two almost exactly
circular small, very thin disks, each mostly composed of paint. Next
they attempt to convert, or map, really, these to bit-strings. For
instance, it might be found that if we create a grid whose squares
are .1 nanometer in length, that we could proceed to have 0 represent
no atom present, and 1 represent an atom present. It may turn out
that these two 2-dimensional grids are then somewhat similar---where
now we align the grid patterns as closely as possible, and do a kind
of "file comparison" (it is hoped that the reader has encountered
software that "diff" two files).

A numerical measure of how similar two 1000x1000 grid patterns
or matrices can be done by a number of measures, but---and this
is the important point---there is a large class of such measures that
all yield approximately the same answer and correspond rather
well with our intuitive feelings (visual impressions) of how similar
two things are.

Using a different strategy, but in the same way, I imagine that 3D
objects could also be "gridded" and then compared. I don't know
what the state of the art is among statisticians these days for doing
this kind of work, but it seems eminently reasonable and actually
rather straightforward (to me).

Any closer to understanding how I think that in principle physical
objects could be mapped to bit strings?

Oh, and one last point. When sending signals into space bit by
bit (literally) some scientists have hit upon the idea of sending
a composite number of pixels (bits), like whatever 2999x3001
is. Now both 2999 and 3001 are prime, and so it's supposed
to occur to some alien that they ought to try to make an almost
square out of it. Then behold! Straight lines and even pictures
emerge. It's not really too different an idea from how TV
images are scanned, I guess.

Anyway, hope this helps explain what I was getting at, and